# Thread: Prove △ADB ≅ △CDB

1. ## Prove △ADB ≅ △CDB

Given:

line segment AB ≅ BC
line segment BC bisects angle ABC

Prove: Prove △ADB ≅ △CDB

I need for someone to show me how to use the statement versus reasons chart.

See picture attachment.

2. Hello, RTC1996!

$\begin{array}{ccc}\text{Given:} & AB \:=\:BC \\
& BD \text{ bisects }\angle ABC\end{array}$

$\text{Prove: }\:\Delta ADB \:\cong\: \Delta CDB$

Code:
              B
*
*|*
* | *
*  |  *
*   |   *
*    |    *
*     |     *
*      |      *
A * * * * * * * * * C
D

$\begin{array}{ccccc}
1. & AB \:=\:BC && 1. & \text{ Given} \\
2. & BD\text{ bisects }\angle ABC && 2. & \text{Given} \\
3. & \angle ABD = \angle CBD && 3. & \text{ d{e}f. angle bisector} \\
4. & BD \:=\:BD && 4.& \text{ Identity postulate} \\
5. & \Delta ADB\:\cong\:\Delta CDB && 5. & \text{ s.a.s.}
\end{array}$

3. Thank you so much. The problem I have with geometric proofs is not knowing which postulates and theorems to use as the reasons for the statements. I have a list of most postulates and theorems but still cannot work them out. How do you do it? What made you come to the conclusion that triangle ADB is congruent to triangle CDB based on the given information and picture? Also, can you do the other proof which I posted yesterday? It seems that no one wanted to tackle the other geometric proof question. What do we need to know to prove that two triangles are congruent?

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### prove that triangle ABD congruent triangle CBD

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